This article is being penned with more than twenty books on billiards by different authors at the; writer's side. In all these books the half ball aim is described as an aim taken through the centre of the cue ball at the edge of the object ball, and this may, we think, be taken as correct beyond cavil or dispute. But in no book, so far as we can ascertain, is the meaning of the term "half-ball" given, much less that of the terms quarter-ball and three-quarter ball. The nearest definition of these aims that we have heard is that, at the moment of contact, and when viewed along the line of aim, half of the cue ball covers or eclipses half of the object ball in the case of a half-ball, a quarter of the cue ball covers or eclipses a quarter of the object ball in the case of a quarter ball, and three-quarters of the cue ball covers or eclipses three-quarters of the object ball in the case of a three-quarter ball.
However this may be it seems to be generally accepted that aim for a half-ball is taken at the edge of the object ball, aim for the quarter ball a quarter diameter outside the edge, and aim for the three-quarter ball a quarter diameter inside the edge.
Now there comes forward Col. C. M. Western, late of the Royal Artillery, in an excellent mathematical work (3s. 6d., Simpkin, Marshall and Co., Ltd.), entitled "The Practical Science of Billiards and its Pointer," who declares—and with no little show of reason, in our judgment— that these aims are misnamed "unless we determine to accept as our datum point a vague point in space one diameter distant from the centre of the object ball and one radius distant from its edge, instead of the centre of the object ball, which is the natural datum point, and which is the point, whatever nomenclature we give the divisions, that the player would, and must, measure from in practice."
Throughout Col. Western's book the half-ball aim is shown as directed at the edge of the object ball, the quarter-ball aim as directed a quarter diameter within the edge and a three-quarter ball aim as directed a quarter diameter outside the edge, thus exactly reversing the accepted nomenclature for the finer and fuller than half-ball aims.
As we have already indicated, there is, in our opinion, much to be said for this revised nomenclature, and even more than Col. Western himself claims for it. For not only is the proposed new naming logical, coherent, and easily remembered, but the same naming, if radius be substituted for diameter, indicates simultaneously the points of aim and contact in the same stroke, a much-needed thing that has not before been done.
What we mean will at once be grasped when it is recollected that contact between cue and object ball always takes place half-way nearer to the centre than the point at which aim is taken. Therefore a half-ball aim at object ball is along a line a half diameter from the centre of the object ball with which contact is made by the cue ball a half radius from the centre; a quarter ball aim at the object ball is taken along a line a quarter diameter from the centre of the object ball, with which contact is made by the cue ball a quarter radius from the centre; and a three-quarter ball aim at the object ball is taken along a line three-quarters of a diameter from the centre of the object ball, with which contact is made three-quarters of a radius from the centre.
Putting the same thing into the plainest possible terms we get:—
Half-ball aim.—Half-ball (or diameter) from centre.
Half-ball contact.—Half-inch (or radius) from centre.
Quarter-ball aim.—Quarter-ball (or diameter) from centre.
Quarter-ball contact.— Quarter-inch (or radius) from centre.
Three-quarter ball aim.—Three-quarter ball (or diameter) from centre.
Three-quarter ball contact.—Three-quarter inch (or radius) from centre.
The same applies, of course, to all other aims, thus:—
Eighth ball aim.—Eighth ball (or diameter) from centre.
Eighth ball contact.—Eighth inch (or radius) from centre.
Three-eighths ball aim.—Three-eighths ball (or diameter) from centre.
Three-eighths ball contact.—Three-eighths inch (or radius) from centre.
Five-eighths ball aim.—Five-eighths ball (or diameter) from centre.
Five-eighths ball contact.—Five-eighths inch (or radius) from centre.
Seven-eighths ball contacts—Seven-eighths inch (or diameter) from centre.
Seven-eighths ball contact.—Seven-eights inch (or radius) from centre.
If the aims and equivalent contacts need to be memorized more easily still, this may be done by working from the centre of the object ball by quarter inches and remembering the contacts as being at the same number of eighths from the centre thus:—
One quarter inch aim makes one eighth inch contact.
Two quarters inch aim makes two eighths inch contact.
Conversely, of course.
One-eighth inch contact requires one-quarter inch aim.
Two-eighths inch contact requires two-quarters inch aim.
It will be found that so coherent a nomenclature cannot be arrived at on any other basis, and we think that the term "quarter-ball" and "three-quarter" ball, as signifying aims; might henceforth very well be reversed.
Meanwhile we invite free correspondence upon this very interesting point and we shall make further references to Col. Western's high informative work.